London’s police force may move from its headquarters, known as New Scotland Yard, as it faces making budget cuts of more than $800 million.

Deputy Commissioner Craig Mackey told the mayor’s office Tuesday that it plans to save $10.5 million a year by moving to a smaller building.

The police headquarters, and its iconic ‘‘New Scotland Yard’’ sign, have been on London’s Victoria Street since 1967. Planned staffing cuts will make the massive central London building a luxury.

Though London’s mayor has the final decision, agreement on the issue between the city’s policing board and the Metropolitan Police makes the move highly likely.

But that does not mean that the HQ of this London institution would vanish without being missed. The chairman of the Metropolitan Police Federation, John Tully, said the sale was like losing the Crown Jewels. ‘‘It’s very regrettable that it’s come to this,’’ he said, quickly suggesting that Mayor Boris Johnson, whose office is in a glass-and-steel building on the River Thames, should reconsider cost-cutting demands.

‘‘The mayor needs to look at his own office,’’ Tully said. ‘‘He sits in a brand-new building on the South Bank. Why doesn’t he sell that to save money?’’

Tully complained the move was an insult — particularly to staff members who have been told ‘‘they’ve got to do more and be better and smarter.’’

Other things being considered to save money are co-locating police with fire service and local authorities and — gasp — they could even end up being based at supermarkets or post offices.